Electrical, I would guess. I've had that problem on Auto Beemers in the past: there's probably some electrical noise (dodgy sensor, bad connections, something like a relay or motor getting silly, etc). What I suspect is happening is that the Auto-box electronics are getting a rogue signal and the program gets spiked - putting you into limp home mode.
When you re-start the car, the problem will return if the fault remains - which is good news (strangely) as it will be so much more traceable :-)
If there is a more or less fixed time for the return to limp home mode, the problem might relate to the car's electrics 'prodding' something on an electrical bus. BMWs tend to have non-critical check control signals that start after critical systems are running (i.e. after you've started and driven off).
In the old days on petrol Beemers, the limp home was induced by faulty ignition coils - and all six needed replacing. Fingers crossed you don't incur that sort of expense!